Title: Surfaces in $\mathbb{P}^4$ lying on small degree hypersurfaces
Abstract:Since the work of Ellingsrud and Peskine at the end of 1980s, it has been known that, with the exception of a finite number of families, smooth compact complex surfaces in $\mathbb{P}^4$ with prescrib...Since the work of Ellingsrud and Peskine at the end of 1980s, it has been known that, with the exception of a finite number of families, smooth compact complex surfaces in $\mathbb{P}^4$ with prescribed Chern classes must lie on hypersurfaces of degree $m\leq 5$. The study of surfaces lying on a small degree hypersurface in $\mathbb{P}^4$---small meaning $\leq5$---seems to be a way of obtaining empirical data leading to a better conceptual understanding of surfaces in $\mathbb{P}^4$. From this perspective, two main issues are considered in the paper:
- an analogue of the Hartshorne-Lichtenbaum finiteness results for smooth surfaces of general type contained in a small degree hypersurface in $\mathbb{P}^4$,
- a study of the irregularity of smooth surfaces contained in a small degree hypersurface in $\mathbb{P}^4$.Read More
Publication Year: 2016
Publication Date: 2016-09-13
Language: en
Type: preprint
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